1. Field
The present invention relates to the field of reservoir modeling. More specifically, the present invention relates to the modeling of hydrocarbon reservoirs having subsurface features such as fractures, faults, and wellbores which may affect reservoir behavior.
2. Background
The production of hydrocarbons such as oil and gas has been performed for numerous years and in many locations worldwide. To produce hydrocarbons, one or more producer wells are drilled into a subsurface formation of a field. Producer wells comprise a borehole that is formed through the earth surface and down to one or more selected formations. The producer wells are completed using long tubular members that serve as casing. A series of casing strings may be run into the borehole and cemented into place. The wells are completed at the level of a hydrocarbon reservoir.
It is desirable to perform computer modeling on hydrocarbon reservoirs in order to simulate and predict fluid flow and recovery from producer wells. Such simulations are oftentimes based on mathematical formulations that are assumed to govern the interrelationship of various numerical values in a reservoir. These values may represent fluid and fluid flow responses such as formation pore pressure, rock porosity, formation permeability and temperature. These values may also be geomechanical responses such as stress or rock deformation.
Numerical methods are oftentimes employed to simulate and analyze activities associated with hydrocarbon recovery or fluid injection. The finite element method is one effective numerical method for this purpose. Such methods provide an approximate numerical solution to complex differential equations which govern the behavior of the reservoir under a given set of conditions.
In finite element analysis for reservoir modeling, a geological system under study is defined by a finite number of individual sub-regions or elements. These elements have a predetermined set of boundary conditions. Creating the elements entails gridding or “meshing” the formation. A mesh is a collection of elements that fill a space, with the elements being representative of a system which resides in that space. The process of dividing a production area under study into elements may be referred to as “discretization” or “mesh generation.”
Finite element methods also use a system of points called nodes. The nodes are placed on geometric shapes which define the elements. The elements are programmed to contain the material properties which define how the structure will react to certain loading conditions. Nodes are placed at a certain density throughout the material under study. For reservoir modeling, changes to the geological system are predicted as fluid pressures or other reservoir values change.
A range of variables can be used in finite element analysis for modeling a reservoir. For fluid flow modeling, reservoir parameters typically include permeability, pressure, reservoir size and, perhaps, temperature. For geomechanical modeling such parameters may include various rock properties such as Poisson's ratio, the modulus of elasticity, shear modulus, Lame′ constant, or combinations thereof. Recently, coupled physics simulators have been developed which seek to combine the effects of both fluid flow parameters and geomechanics to generate reservoir responses.
In conventional numerical studies for reservoir simulation, it is important to explicitly track the geometrical shape of the formation under analysis. This means that the elements honor the geometry of the formation. However, the use of finite elements in reservoir modeling is challenged by the presence of subsurface features. In this respect, hydrocarbon reservoirs under production typically contain various forms of natural or man-made subsurface features. Examples of natural subsurface features include faults, natural fractures and formation stratification. Examples of man-made features include perforations from wellbores, fracture wings of a fractured wellbore completion, and wormholes due to acid injection activities. These features create discontinuities that affect reservoir behavior.
Reservoir simulation is also challenged where high gradients of reservoir properties exist. An example of a subsurface feature that presents a high gradient is a wellbore. The wellbore, when viewed as a singular line source or sink for pore pressure, can cause high pressure gradients in the near-well region. Fluid flow and pressure gradients that exist radially around a wellbore are steep. Modeling such gradients generally requires the use of a high density mesh.
Conventional numerical simulators require a grid system that honors the geography of the discontinuity or high gradient area. However, from a geometric standpoint, finite element methods generally prefer a structured mesh. The existence of arbitrarily shaped subsurface features makes it difficult to build a structured mesh. Constructing a high quality mesh for each geometrical variation may require significant man-power and considerable expertise. Failure to honor transmissible boundaries created by wormholes, fractures, stratification breaks and the like can cause post-production reservoir simulations to be inaccurate.
Yet another problem with mesh generating solutions relates to the fact that man-made subsurface structures will change over the life of a reservoir. Evolving subsurface features include newly formed wellbores, wormhole growth or injection-induced fracture growth. Such features require the mesh or grid to evolve accordingly to accommodate the varying geometry of subsurface features. During this mesh evolution process, parameter values which have been stored at nodes or element locations need to be mapped into the appropriate locations in the new mesh. This process may result in loss of precision.
Therefore, a need exists for an improved numerical method that can closely capture the effects on hydrocarbon reservoir modeling introduced by subsurface features. A need further exists for an improved method for modeling a reservoir that allows a computational mesh to remain unaltered regardless of varying geometries of subsurface features. A need exists also for a method for modeling reservoir response in a subsurface system wherein a finite element mesh is created within physical boundaries that need not honor the geometry of a subsurface feature.